In the coordinate plane, a circle centered on point (-3, -4) passes th

Question

In the coordinate plane, a circle centered on point (-3, -4) passes through point (1, 1). What is the area of the circle?

A. 9π
B. 18π
C. 25π
D. 37π
E. 41π

Kudos for a correct  solution .

BrainLab · Answer

We can build a triangle with the given points and find the hypotenuse (Radius) using Pythagorean theorem:
4^2+5^2=r^2 --> 16+25 so the area is equal to 41Pi Answer (E)

thembaseeker · Answer

r^2=(-3-1)^2+(-4-1)^2=16+25=41

Area of circle=πr^2=41π

Answer : E

m2k · Answer

The circle is with center (-3,-4) and one of the point as (1,1).Using distance equation we can get the radius :
r^2 = sqrt ((-3-1)^2 + (-4-1)^2) or r = 41^1/2

Hence aread = pi (r)^2 = 41 pi

kunlmhjn · Answer

From the distance formula: r^2= (-3-1)^2 + (-4-1)^2 r^2= 16+25=41 As we know, Area of a Circle=pi * r^2 Therefore, Area of Circle= 41 pi Hence, the answer is 'E' :-D

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

As you know, the area of a circle is  π(r)^2 , meaning that your goal is to find the radius of this circle. To go from the center of the circle (-3, -4) to the given point on the circle (1, 1), you move 4 spaces horizontally (from x-coordinate -3 to x-coordinate 1) and 5 spaces vertically (from y-coordinate -4 to y-coordinate 1). That sets up a right triangle in which the hypotenuse is the radius. a^2+b^2=c^2 becomes 4^2+5^2=c^2, so c^2=16+25=41. And here's where a shortcut awaits. Since your job is to take the radius (c in the Pythagorean Theorem) and square it, then multiply by π (π(r)^2) you're actually about done. Since  r^2=41 , the answer is  41π .

LogicGuru1 · Answer

Apply distance formula between the xy pair of (-3-,4) and (1,1)
The distance so obtained will be the radius of the circle
Once radius is known then  area = π*r^2

D= \sqrt{(-3-1)^2+(-4-1)^2} 
 D= \sqrt{(-4)^2+(-5)^2}

D= \sqrt{16+25}

D= \sqrt{41}

Radius = \sqrt{41} 
 Radius^2 = 41

Area = Radius^2*π

Area= 41π

Answer is E

In the coordinate plane, a circle centered on point (-3, -4) passes th

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GMAT Problem Solving (PS) Questions

In the coordinate plane, a circle centered on point (-3, -4) passes th

Prep Toolkit

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